Parasurface groups

Khalid Bou-Rabee

Vol. 248 (2010), No. 1, 23–30

DOI: 10.2140/pjm.2010.248.23

Abstract

A residually nilpotent group is k-parafree if all of its lower central series quotients match those of a free group of rank k. Magnus proved that k-parafree groups of rank k are themselves free. We mimic this theory with surface groups playing the role of free groups. Our main result shows that the analog of Magnus’ theorem is false in this setting.

Keywords

Magnus’ theorem, Magnus’ conjugacy theorem, parasurface, parafree, almost surface groups, automorphism-nilpotent separable

Mathematical Subject Classification 2000

Primary: 20F22

Milestones

Received: 12 August 2009

Revised: 6 December 2009

Accepted: 17 December 2009

Published: 1 October 2010